Enhanced superconducting transition temperature in electroplated rhenium

ABSTRACT

This disclosure describes systems, methods, and apparatus for multilayer superconducting structures comprising electroplated Rhenium, where the Rhenium operates in a superconducting regime at or above 4.2 K, or above 1.8 K where specific temperatures and times of annealing have occurred. The structure can include at least a first conductive layer applied to a substrate, where the Rhenium layer is electroplated to the first layer. A third layer formed from the same or a different conductor as the first layer can be formed atop the Rhenium layer.

CLAIM OF PRIORITY UNDER 35 U.S.C. § 119

The present application for patent is a Continuation of U.S. patentapplication Ser. No. 16/289,599 entitled “Enhanced SuperconductingTransition Temperature in Electroplated Rhenium” filed Feb. 28, 2019which claims priority to Provisional Application No. 62/636,611 entitled“Enhanced Superconducting Transition Temperature in ElectroplatedRhenium” filed Feb. 28, 2018, as well as Provisional Application No.62/727,825 entitled, “Enhanced Superconducting Transition Temperature inElectroplated Rhenium” filed Sep. 6, 2018. These applications areassigned to the assignee hereof and hereby expressly incorporated byreference herein.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with government support under Grant Number70NANB14H095 awarded by NIDT. The government has certain rights in theinvention.

FIELD OF THE DISCLOSURE

The present disclosure relates generally to superconductors. Inparticular, but not by way of limitation, the present disclosure relatesto systems, methods and apparatuses for electroplating Rhenium andoperating resulting devices in a superconducting regime.

DESCRIPTION OF RELATED ART

In all subsequent references, the terms “Rhenium” and “Re” areinterchangeable and refer to any pure rhenium film or alloy thereof.

Versatile superconducting materials are important in order to continuethe progress of high speed classical [1-4] and quantum computers [5] aswell as a wide range of information technology and low temperatureresearch in general. In particular, it is important to develop materialsthat are readily transferable to manufacturing, i.e., that can be usedin combination with standard fabrication and interconnect techniques toreduce power dissipation and heating. Another critical metric is arelatively high critical temperature (T_(c)). With the advent oflow-power, closed cycle cooling platforms, it is straightforward toobtain temperatures down to 2.2 K [6, 7], while the 4.2 K liquid-Hebarrier is more relevant to general-purpose low temperaturemeasurements. In either case, it is desired that the criticaltemperature (T_(c)) be well above the base or operating temperature inorder to maintain a high critical current and avoid loss due toquasiparticles.

To that end, there is a small subset of existing superconductingmaterials that can be used for this application. In general,state-of-the-art materials include Nb and its binary and ternary alloyssuch as Nb—N, Nb—Ti and Nb—Ti—N. These materials all are useful in termsof high T_(c), can be used in bulk or deposited as thin films, and canbe connected using ultrasonic-wirebonding techniques. However, they tendto be difficult to work with mechanically and have poor solderingproperties due to strong oxidation. While workarounds to these problemsexist, they are not easily integrated into standard circuit fabrication.

Other typical materials (e.g., Pb, In, Sb, Al, Re, high T_(c) oxides,etc.) suffer from toxicity, low melting temperatures, low criticaltemperatures, oxidation, contact resistance, can't be deposited viaaqueous electroplating, incompatibility with wirebonding/soldering,incompatibility with multilayer circuit boards. To date, no one solutionhas emerged that addresses all the desired properties.

SUMMARY OF THE DISCLOSURE

The following presents a simplified summary relating to one or moreaspects and/or embodiments disclosed herein. As such, the followingsummary should not be considered an extensive overview relating to allcontemplated aspects and/or embodiments, nor should the followingsummary be regarded to identify key or critical elements relating to allcontemplated aspects and/or embodiments or to delineate the scopeassociated with any particular aspect and/or embodiment. Accordingly,the following summary has the sole purpose to present certain conceptsrelating to one or more aspects and/or embodiments relating to themechanisms disclosed herein in a simplified form to precede the detaileddescription presented below.

Some embodiments of the disclosure may be characterized as asuperconducting circuit system comprising: a means for maintaining avacuum; a means for maintaining the circuit at or below 4.2 K; asubstrate; a first conductive layer bonded to the substrate; a second Relayer; and a third conductive layer. The second Re layer can be bondedbonded to the first layer via electroplating. The second Re layer canalso have a thickness of between 10 nm and 1000 nm, and can be patternedto create at least a portion of the superconducting circuit. The thirdconductive layer can be bonded to the second Re layer and canencapsulate the second Re layer. The first, second, and third layers canoptionally be patterned to form a portion of the superconductingcircuit. Further, the encapsulation of the Re layer can be done toprevent oxidation of a surface of the Re layer.

Other embodiments of the disclosure may also be characterized as amethod of fabricating a superconducting circuit that is superconductingat or above 4.2 K. The method can include providing a substrate;applying a first conductive layer onto the substrate; electroplating asecond Re layer above the first layer to a thickness of between 10 nm to1000 nm; applying a third conductive layer onto the second Re layer andencapsulating the second Re layer to prevent oxidization of the secondRe layer; making a wire bond or solder connection between the thirdlayer and another circuit; and arranging the superconducting circuitwithin a vacuum chamber configured to cool the superconducting circuitto at least 4.2 K. The first, second, and third layers can optionally bepatterned to form a portion of the semiconducting circuit.

BRIEF DESCRIPTION OF THE DRAWINGS

Various objects and advantages and a more complete understanding of thepresent disclosure are apparent and more readily appreciated byreferring to the following detailed description and to the appendedclaims when taken in conjunction with the accompanying drawings:

FIG. 1a illustrates data from References 10, 12 showing T_(c)(Re) fromthe literature;

FIG. 1b illustrates a comparison of critical behavior for Re in Cu, Au,and Pd multilayers, for Samples 5-7;

FIG. 2 illustrates critical current J_(c) vs. normalized temperaturet=T/T_(c) for as-prepared electroplated multilayer, (Au/Re) x10/Au/PTFE,Sample 5 (10 multilayers of Re and Au atop an Au layer atop PTFE);

FIG. 3(a) shows zero-field cooled (ZFC) and field-cooled (FC) magneticmoment as functions of increasing temperature measured in μ₀H=0.5 mT;

FIG. 3(b) shows a magnetic hysteresis loop measured at T=1.8 K;

FIG. 4 shows a quality factor of Au/(Re/Au)×10/Cu/PTFE (Sample 5)compared to bare Cu/PTFE on a grounded coplanar resonator;

FIG. 5 illustrates an embodiment of a method for using a high-Tcmultilayer circuit;

FIG. 6 illustrates an embodiment of a method for fabricating asuperconducting circuit that is superconducting at or above 4.2 K;

FIG. 7A shows a cross section of a multilayer planar structure, such aswould be applied to a printed circuit board;

FIG. 7B shows a cross section of a multilayer planar structure such aswould be applied to form a wire or cable;

FIG. 8 shows a STEM image of an Mx-Re-My multilayer;

FIG. 9 shows another STEM image of an Mx-Re-My multilayer;

FIG. 10 shows a pair of TEM images of an Mx-Re-My multilayer;

FIG. 11 shows another STEM image of an Mx-Re-My multilayer;

FIG. 12 shows another STEM image of an Mx-Re-My multilayer;

FIG. 13 shows another STEM image of an Mx-Re-My multilayer;

FIG. 14 shows another STEM image of an Mx-Re-My multilayer;

FIG. 15 shows another STEM image of an Mx-Re-My multilayer;

FIG. 16 illustrates an embodiment of a via structure in a multilayer PCBor other multilayer circuit board using a superconducting via that iscoated after the multilayer structure has been laminated;

FIG. 17 illustrates another embodiment of a via structure in amultilayer PCB or other multilayer circuit board using a superconductingvia that is coated after the multilayer structure has been laminated;

FIG. 18 illustrates an embodiment of a superconducting resonance cavitywith an inner wall formed from a thin low-T_(c) superconductor that isproximitized by a good electrical bond with a high-T_(c) superconductor;and

FIG. 19 illustrates a superconducting circuit system.

DETAILED DESCRIPTION

Preliminary note: the flowcharts and block diagrams in the followingFigures illustrate the architecture, functionality, and operation ofpossible implementations of systems and methods according to variousembodiments of the present invention. It should also be noted that, insome alternative implementations, the functions noted in the block mayoccur out of the order noted in the figures. For example, two blocksshown in succession may, in fact, be executed substantiallyconcurrently, or the blocks may sometimes be executed in the reverseorder, depending upon the functionality involved.

One superconducting element in the group that suffers from low criticaltemperatures, Re, stood out as a promising candidate for improvement ofthe critical temperature, T_(C). Re is a transition metal that isresistant to oxidation with a high melting temperature of 3186° C. [8].It is used widely in various industrial and scientific applications suchas strengthening materials and in high temperature thermocouples. Whileepitaxial Re can be used for low-loss RF-resonators in qubit circuits[9], it has no specific advantage over other more traditionalsuperconducting materials. In particular, the critical temperature ofcrystalline-Re is relatively low, T_(c)(Re)˜1.7 K [10].

The word “exemplary” is used herein to mean “serving as an example,instance, or illustration.” Any embodiment described herein as“exemplary” is not necessarily to be construed as preferred oradvantageous over other embodiments.

This disclosure describes superconducting circuits (includingsuperconducting circuit boards, electronic devices, systems ofelectronic devices), and methods of manufacturing superconductingcircuits, where the superconducting circuits (hereinafter “circuits”)exhibit either a high critical temperature T_(c) (e.g., higher than 1.8K for annealed Re films and greater than 4.2 K for unannealed films). Inan embodiment, the circuit can include at least one conductor or lead(hereinafter “conductor”), wherein the conductor is formed from“multilayers,” where each multilayer includes a buried Re layerelectroplated on another conductor that is compatible withelectroplating. Examples of such conductors include, but are not limitedto, Cu, Au, Pt, Pd, Ni, Rh, Ru, or conductive seed layers on varioussubstrates including metal, PTFE, FR4, plastic, Si, system-on-chip,sapphire, quartz, doped semiconductor, or polyimide. The increased T_(c)in Re layers electroplated on non-ferromagnetic conductors such as Au,is unexpected [10-12]. However, because pure Re is immiscible (e.g.,less than 1% or less than 0.1%) in standard microelectronics metals(e.g., Cu, Au, Pt, Pd, Ni, Rh, Ru) it forms a discrete film whenelectroplated on standard microelectronics metals such as Au and Cu. Inother words, some superconducting materials alloy with standardmicroelectronics metals, and the resulting alloy may losesuperconductivity or result in a degraded superconductor (e.g., lowerT_(c)).

For Re films, if annealed, the T_(c) can be 1.8 K. Although this T_(c)is lower than for non-heated Re films, this lower T_(c) is still usefulfor applications at very low temperature (less than 100 mK). However, anelectroplated Re film that is not annealed can exhibit T_(c) greaterthan 4.2 K, meaning that it can be used with mere liquid He coolant.Refrigeration vessels, coolants, complexity, and time to cool are allimproved at 4.2 K over very low temperature applications (e.g., 2.2 K),and so the discovery of a high-T_(c) film that can be electroplated viaaqueous solutions is highly valuable to the industry. Thisenhanced/increased T_(c) may be due to the amorphous structure of the Refilm, hydrogen incorporation in the Re film, or strain in the Re film,or a combination thereof. In an embodiment, once the third conductivelayer is applied, the superconducting circuit can be annealed at100-150° C. for 1-10 minutes. However, annealing at greater than 150° C.for any length of time may degrade T_(c).

Another unexpected aspect of electroplating Re on certain conductors isthat Re is relatively immiscible with, common microelectronicsconductors, for example Cu, Au, Pt, Pd, Ni, Rh, Ru. For instance, theherein disclosed electroplated Re may experience less than 1% or lessthan 0.1% miscibility with adjoining layers formed from commonmicroelectronics conductors such as Cu, Au, Pt, Pd, Ni, Rh, Ru. Forinstance, see “Constitution of Binary Alloys, Max Hansen; Rodney PElliott; Francis A Shunk; Research Institute. New York, McGraw-Hill,1958.”

Re may form surface oxide films when exposed, and thus finishing themultilayer with a layer other than Re can improve performance. Forinstance, in a Mx-Re-My multilayer structure, where “Mx” and “My” denotesome metal other than Re and Mx can be the same metal as My, the finallayer My, can be some metal that resists oxidation (e.g., Au). The Mxand My layers need not be the same.

A multilayer can be described as a sandwich of a conductor, Re, and aconductor or Mx-Re-My. Multilayers comprise two or more of theseMx-Re-My sandwiches. The thickness of each Re layer can be less than 200nm. For instance, the Re layer thickness can be less than 150 nm, orless than 100 nm, or less than 75 nm, or less than 50 nm, or less than25 nm. Cracks in the Re layer may occur if the Re layers are too thick.Alternatively, if the Re is too thin it will not be superconducting dueto proximization from the capping layer. Accordingly, the Re layers canpreferably be thicker than about 10 nm. In an embodiment, a conductorcan include multilayers (e.g., 1-3), where a multilayer includes a Relayer and a conductor (e.g., Au) layer. For instance, 3 multilayerswould include three Re layers and 3 conductor layers, arranged inalternating layers. 1-3 multilayers may be preferable for conductorsused in DC circuits. In another embodiment, 3-10 multilayers may beimplemented, for instance in RF circuits. In other embodiments, 10-20multilayers can be implemented. In some circuits, certain conductors mayhave a first number of multilayers (e.g., 1-3), while other conductorshave a second number of multilayers (e.g., 3-10 or 3-20). Each conductorlayer can be between 50 nm and 500 nm. In one embodiment, depositiontime can be used to control layer thickness.

In an embodiment, a Re layer can be electro-deposited (e.g.,electroplated) using any method that results in a smooth, continuousfilm using a DC or pulsed power supply, and can be deposited atatmospheric pressure. The power supply can be set to a constant-currentmode and at a power of, for instance, 8 A/dm². Electroplating can alsouse a potentiostatic control. In an embodiment, solutions with differentconcentrations of Re can be electroplated in different layers or indifferent locations throughout a circuit. The electroplating can occurwithin an aqueous solution containing 11 g/L of KReO₄ with the pHadjusted to 0.9 using, for instance, sulfuric acid. In an embodiment,the recipe in C. G. Fink and P. Deren, Trans. Electrochem. Soc. 66, 471(1934) can be used. The anodes can be, but are not limited to,platinized titanium. Moderate stirring can be performed with a magneticbar coated with polytetrafluoroethylene (PTFE). This stirring can occuron a hot-plate stirrer at temperatures of 25-30° C. In tests, the Redeposits were shiny and smooth, typically dark gray, with good adhesion.Test samples with a variety of layer compositions are reported in TableI below:

Layer Sample Bottom Middle Top 1 Vacuum deposited 200 Au 300 Re 100 Autrilayer on Si 2 Electroplated 200 Au 300 Re n/a bilayer on Si 3Electroplated 200 Au 300 Re  75 Au trilayer on Si 4 Electroplated 200 Au(20 An + 75  75 Au multilayer on Si Re) × 10 5 Electroplated 200 Au (20Au + 75  75 Au multilayer Re) × 10 on Cu/PTFE 6 Electroplated N/A (500Cu + 75 500 Cu multilayer Be) ×5 on Cu/PTFE 7 Electroplated N/A (500Pd + 75 500 Pd multilayer Re) × 5 on Cu/PTFE

TABLE I shows sample composition and thicknesses (nm). For sample 1, aquartz crystal thickness monitor was used. For sample 3 and 4,thicknesses were obtained directly from STEM. Samples 2, 5, 6 arenominal thicknesses based on times derived from 3 and 4. The Au, Cu, andPd was grown using standard electroplating solutions with the exceptionsbeing the Au metallization with a 5 nm Ti adhesion layer on the Si in2-4, and the vacuum prepared trilayers for 1.

The multilayer can be formed or arranged atop a second conductor, whichmay or may not be identical to the conductor within the multilayer. Forinstance, a Re—Au multilayer may be formed or arranged atop a Cu layer.The combination of second conductor with a Re-My (where My is anypreferred conductor as discussed earlier) multilayer above forms aconductor, and this conductor can be formed or arranged on a substrate(e.g., a circuit board made from FR4, PTFE, or polyimide, an integratedcircuit, a doped semiconductor, or a System-on-Chip) such as Si or PCBto name two non-limiting examples. Sapphire, quartz, and PFTE are otherpossible, but non-limiting, substrate or circuit board materials. Inother embodiments, the conductor may be free-floating or notformed/arranged on a substrate (e.g., tower-mounted power lines orconductors used in superconducting magnets). In these instances, thesecond conductor may have a circular or ovular cross section and have amultilayer formed around this inner second conductor such that themultilayer extends radially out from a longitudinal center of the secondconductor. Such free-floating conductors can be a 5^(th) to 10,000^(th)of an inch in diameter. In some cases, the free-floating conductor mayinclude multiple strands of conductor, each coated with one or moreRe-My multilayers, where the multilayer-coated strands are wound aroundeach other in a spiral arrangement to form a larger conductor bundle. Insome cases, the Re-My-multilayer-coated conductors can be arranged asstrands with NiTi or other type strands to form a larger hybridconductor bundle. In the case of vias, the multilayer can be formed onan inside surface of the second conductor (e.g., see FIG. 16), since thesecond conductor forms a donut-shape within the via.

The resulting conductor (e.g., Re), whether as an isolated strand, or aspart of a bundled conductor, a circuit, a circuit board, a flex circuit,an electrical device, or a system of electrical devices, is a Type-IIsuperconductor (crystalline Re is a Type I superconductor) with highT_(c), high critical-current densities, and low RF losses. Althoughhigh-T_(c) often refers to critical temperatures above the liquidnitrogen 77 K point, for the purposes of this disclosure, “high-T_(c)”means a critical temperature above Rhenium's latent 1.7 K criticaltemperature. In some cases, electroplating Re causes a shift in T_(c) upto as high as about 4.2 K, or 4.4 K, or 5.0 K, or 6.0 K, or 6.5 K. Thisshift is thought to be a byproduct of either hydrogen incorporation intothe Re or that the Re becomes amorphous and/or strained, or anycombination of these effects, that occurs during electroplating.

Once the multilayer is formed on the second conductor to form aconductor (or a bundled conductor, a circuit, a circuit board, anelectrical device, or a system of electrical devices), heating oradditional heating may occur (e.g., conductor bonding or annealing).Unexpectedly, the T_(c) was found to improve, well above 4.2 K (thetemperature of liquid helium) when annealing temperatures up to 100° C.,or up to 150° C., were applied to the multilayer. However, above 150° C.the T_(c) may begin to drop. Further, it was found that annealingbetween 100° C. and 150° C. could increase T_(c) when applied for up toone hour (or up to 10 minutes), but degraded T_(c) when heat was appliedfor longer than one hour. Test results showed up to a 0.4 K increase inT_(c) via annealing with 6.3 K being the highest T_(c) observed for theRe-My multilayers tested

The herein disclosed circuit can comprise a multitude of the describedconductors, connectors, and reactive and/or resistive components. Thecircuit can be arranged within a vacuum chamber, and a vacuum device canbe used to create a sub-atmospheric or vacuum environment for thecircuit. The circuit can be cooled to below the critical temperature ofany Re-MX multilayers in the circuit. This critical temperature istypically about 2.2 K, or about 3.6 K, or about 4.0 K, or about 4.7 K,or about 5.5 K for circuits that have not been heated to higher than150° C. for more than one minute, and less than 1.8 K for circuits thathave been heated to higher than 150° C. for more than one minute. Thecritical temperature is often less than 5.5 K for circuits that have notbeen heated to higher than 150° C. for more than one minute. At the sametime, the critical temperature can be enhanced, or increased, whenelectroplated Re is annealed to between 100° C. and 150° C. for 1-10minutes. Heating above this range or for longer than one to ten minutestends to degrade T_(c). An assembly can include a cooling device, whichalong with a vacuum device, can achieve these low temperatures. In anembodiment, the system can include a multilayer-coated conductor eitherfree floating or on a substrate forming a portion of a circuit atsub-atmospheric pressure (e.g., vacuum) within a vacuum chamber wherepressure is controlled by a vacuum device, and further where temperatureis maintained within a range just above 2 K or 4 K by a cooling device.

To test the T_(c) and other values of the herein disclosed multilayers,the inventors first grew a reference, Sample 1, of Au/Re/Au/prime-Si invacuum using e-beam evaporation for the Au and sputter-deposition forthe Re. This sample was used to compare against standard Re preparationmethods.

Electroplated bilayers, trilayers, and multilayers of Re and Au wherethen grown on vacuum-prepared Au/Si substrates, Samples 2-4 in Table I.A 20 nm seed of electroplated Au was typically applied before the Re.

Finally, multilayers of Re/Cu/Re/Au, and Re/Pd were electroplateddirectly onto commercial Cu/PTFE circuit boards Samples 5-6. The boardswere also patterned with resonators in order to test the RF propertiesof the multilayers. PTFE was used for its low loss tangent, tanδ=6.8×10⁻⁴, at 15 K. J. Mazierska, M. V. Jacob, D. Ledenyov, and J.Krupk, in 2005 Asia-Pacific Microwave Conference Proceedings (2005),vol. 4, p. 2370.

Of particular concern in many low-temperature measurements is theDC-resistance and RF-loss that can create ohmic heating and degradationof quantum information. Therefore, the inventors characterized bothtypes of transport properties. The measurements were conducted in both aliquid-He dewar-based system and an adiabatic demagnetizationrefrigerator (ADR). The samples on Si were measured with a de 4-pointprobe. For the films on the 35-μm-thick copper traces, it was necessaryto use ac-transport with a lock-in amplifier due to their lowresistance.

The resistivity of the sputtered-Re layers on Si was measured on 0.6 mmslices cleaved from 5-mm-wide strips. The T_(c) was taken to be thefirst inflection point in the R vs. T curves. Samples were contacted byeither wirebonding (25 μm Al wire for low current measurements) orsoldering (standard Cu wire for high current measurements). All samplescould be soldered using 60:40 SnPb. No problems were encounteredwirebonding to the thick Cu while for the Pd- and Au-capped samples Alwirebonds did not adhere as well.

Turning to the data, for the sputter-deposited Re samples the inventorssaw a sharp transition to zero resistance in FIG. 1(a)(1), with T_(c)slightly exceeding that of the highly strained Re from Reference 10.This can be attributed to Au—Re interfacial strain that tends to expandthe Re unit cell. Subsequent high temperature annealing, up to 400° C.,of this sample showed that T_(c) is stable within 0.1 K. This is in linewith the high melting temperature of Re and its immiscibility with Au[24-26]. FIG. 1 illustrates resistance vs. temperature. FIG. 1(a)illustrates data from References 10, 12 showing T_(c)(Re) from theliterature. Curves show data from Au/Re samples described in Table I.FIG. 1(b) illustrates a comparison of critical behavior for Re in Cu,Au, and Pd multilayers, for Samples 5-7.

More surprisingly, and unlike the sputter-deposited Re samples, for theelectroplated samples on Si, a progression of T_(c) up to approximately6 K was obtained. First, with the Re/Au bilayer sample in FIG. 1(a)(2)(note that this is a non-capped bi-layer), the inventors measured arange of critical temperatures from T=4.3 K to 4.7 K. These samples tendto tarnish over a period of a few weeks due to the exposed Re surface.Therefore, the inventors moved to capping the samples with electroplatedAu films (e.g., see FIG. 1(a)(3)-(5)). This resulted in more stablefilms and reproducible T_(c) measurements. Moreover, T_(c) in theselayered samples increased to T>5.7 K, with multiple steps in thetransition in some samples, as shown in FIG. 1(a)(3). Experiments onthese films, including sputtering the top Au film off and using muchthicker Au layers, tend to depress the T_(c). Subsequent samples grownas multilayers on Si, FIG. 1(a)(4), demonstrated even higherreproducibility and enhancement of T_(c).

The inventors then looked at the multilayered films on commercialcircuit boards, FIG. 1 (a)(5). Here, as T decreases one sees the firstdrop in the resistance for T_(c)˜6.1 K. However, there are slight stepsin these transitions with low resistance tails. The tails go down anadditional 0.1-0.5 K, depending on the current, before the transition tozero resistance.

In light of the variation of T_(c)(Re) (possibly due to strain), asoutlined above, the properties of the Re grown with a series of metalfilms (e.g., Cu, Au, and Pd) was compared. These metals all share aclose-packed structure, fcc, that is similar to the hcp structure of Re.However, the nearest-neighbor distance in the close-packed plane forthese three is 0.256, 0.275, and 0.288 nm [27], respectively. This spanscompressive, low, and expansive strain relative to the 0.274 nmnear-neighbor spacing for elemental Re [27]. As shown in FIG. 1(b), allthree types of multilayered films demonstrate the enhancement of T_(c).Both Re/Au and Re/Cu have a sharp drop in resistance well above 6 K,whereas the Re/Pd samples have a slightly lower, more roundedtransition. This may be due to the fact that Re, Cu, and Au areimmiscible, while RePd tends to alloy [25].

Versatility in connecting to the samples (e.g., soldering orwirebonding) was important in that this flexibility allows one toachieve good thermalization while high current densities, J are appliedthrough the soldered contacts. In the same measurement, voltage leadscould be wirebonded, as shown in the inset of FIG. 2. For samples on Sisubstrates the inventors measured critical current J_(c)˜2.5 to 5×10⁸A/m² for trilayers and multilayers, respectively. For films on Cu/PTFE,data in FIG. 2, the inventors saw lower J, 10⁷ A/m² due to the lowtemperature tails.

FIG. 2 illustrates critical current J_(c) vs. normalized temperaturet=T/T_(c) for as-prepared electroplated multilayer, (Au/Re)×10/Au/PTFE,Sample 5 (10 multilayers of Re and Au atop an Au layer atop PTFE). Theinset shows two samples mounted; bottom sample with current leadssoldered for high currents and voltage leads wirebonded; top sample iswirebonded on both current and voltage leads.

While it is significant that the resistance drops to zero, it does notunequivocally demonstrate that the films are superconducting over theirentire area. Magnetic measurements, which access two dimensions, areable to distinguish this behavior. For this study, the Au/(AuRe)×10/Simultilayer film, Sample 4, was cleaved into a rectangular sample, 5.0mm×5.6 mm, for measurement in a magnetometer based on a superconductingquantum interference device (SQUID). In magnetic measurements ofsuperconductors, the apparent magnetic moment is due to the fieldproduced by shielding currents and trapped magnetic flux. The moment wasmeasured in a perpendicular field of μ₀H=0.5 mT as a function ofincreasing temperature after cooling in zero field (ZFC), and aftercooling in a field (FC) of μ₀H=0.5 mT, FIG. 3(a). The criticaltemperature, T_(c)˜5.4 K, is the end point of the broad transition fromthe shielding state to the normal state seen in the ZFC curve. Thepositive FC moment values for T<T_(c) are indicative of an incompleteMeissner effect (incomplete expulsion of magnetic flux upon coolingbelow T_(c)), which is characteristic of type-II superconductors [28].

FIG. 3 illustrates a magnetic moment study of Sample 3. FIG. 3(a) showszero-field cooled (ZFC) and field-cooled (FC) magnetic moment asfunctions of increasing temperature measured in μ₀H=0.5 mT. The criticaltemperature is T_(c)=5.4 K. FIG. 3(b) shows a magnetic hysteresis loopmeasured at T=1.8 K. The initial field is shown with an increasingcurve. The upper critical field is μ₀H_(c2)˜2.5 T. The inset shows adetail of the initial curve, which suggests a lower critical field ofμ₀H_(c1)˜2 mT

A hysteresis loop of magnetic moment as a function of field was measuredat T=1.8 K, FIG. 3(b). The shape of the loop is characteristic oftype-II superconductors [28]. The magnetic moment approaches zero at anupper critical field μ₀H_(c2)˜2.5 T. Symmetrical flux jumps are evidentin the descending branches of the hysteresis loop. A low-field detail ofthe initial curve is shown in the inset suggesting a small lowercritical field μ₀H_(c2)˜2 mT.

For most superconducting applications, notably SQUID magnetometry andquantum computing, it is also important to establish that the filmsmaintain low loss at RF into the GHz regime. Therefore, resonator losstangent, tan δ=1/Q_(T) vs. temperature was compared for Au/Re plated(sample 5) vs. bare copper traces. Here, Q_(T) is the total qualityfactor of the resonator. The samples were placed in a magneticallyshielded environment and cooled to low temperature. The RF measurementswere made using a vector network analyzer. The Q_(T) was determinedusing a Lorentzian fit [29] to the resonance from a 18.2 mm×longgrounded-coplanar-waveguide resonator on a 0.59 mm thick PTFE board. Thewidth and gap of the resonator were 0.81 and 0.076 mm, respectively. Thecoupling quality factor of the resonator to the feedline, Q_(C)˜2×10⁴.Because the Q_(T) was significantly lower than Q_(C), the internal losstan δ_(i)=1/Q_(i)˜1/Q_(T), where Q_(i) is the internal quality factor.As shown in FIG. 4, for the bare copper board tan δ_(i)˜2×10⁻³ for T<8K. Below about T=250 mK a slight increase appears. This increase isconsistent with two-level system (TLS) loss [30], most likely in thePTFE.

For the Re/Au electroplated circuit board, on the other hand, a decreasefor tan δ_(i) of T<5 K is seen in FIG. 4. This is expected in the caseof a superconducting transition in the Re—Au plating. The loss drops tothat of PTFE at low temperature [22], and the TLS increase appears againat very low temperature. This shows that the loss is limited by thematerial of the circuit board rather than the metal traces. Therefore,development of new, low-loss board materials is now an importantconsideration for these circuits. On the other hand, these data showthat plating of metallic components will significantly improve theirperformance at RF as well as DC.

FIG. 4 shows a quality factor of Au/(Re/Au)×10/Cu/PTFE (Sample 5)compared to bare Cu/PTFE on a grounded coplanar resonator. The insetshows an Au/Re circuit board soldered in a Au-plated Cu boxconnectorized with SMA ports.

Preliminary STEM studies (see FIGS. 8-15) show high transmission throughthe Re layers with a striated pattern perpendicular to the plane. Theinventors' own density-functional-theory calculations confirm theimmiscibility of Au/Re and point to the possibility of an increase inthe density of states near E_(p) as the Re lattice expands, in agreementwith Reference 12.

There is a wide spectrum of components (e.g., circuits, circuit boards,electrical devices, interconnects, cables, and shields) that canimmediately benefit from the herein disclosed superconductingelectrodeposited Mx-Re-My multilayers, with the thickness of Re beingtypically 10 nm<t<1000 nm, and Mx and/or My being preferentially Au butcan be any of a number of non-ferromagnetic, electro-plateable metalssuch as Cu, Au, Pt, Pd, Ni, Rh, Ru. In other words, thenon-ferromagnetic layers can be the same or different. In oneembodiment, the base non-ferromagnetic layer, Mx, can be a firstmaterial, and all subsequent non-ferromagnetic layers, My, can be asecond and different material. In this context, components include anypart of a circuit configured to conduct electrical current, including,but not limited to: circuit boards (i.e. metalized dielectrics that mayor may not be patterned), flexible circuit boards, conductors (longstrands of conductors that may or may not be insulated), cables (bundlesof conductors that may or may not be insulated), coaxial cables (eitherthe center conductor is plated or both the shield and center conductorplated) (braided or semi-flexible), vacuum feedthroughs, resonancecavities, electrostatic shields, and any type of connector pins (eithermale or female) that go between components, including “fuzzbuttons”. Asanother example, a superconducting integrated circuit may includecomponents designed for magnetometry and/or thermometry for which it isdesirable that the critical current be higher than it is for othercomponents (e.g., processor components such as qubits) of the circuit.As another example, a superconducting integrated circuit may includecertain components made of a first material or set of materials thatproduce less noise than other components made of a second material orset of materials. In some embodiments, the Mx and My layers may beelectro-platable.

Components that are included fall into two general types that are usedfor different operational temperature ranges, T_(op): (1) Componentsthat have not been annealed or heated under conditions (e.g., above acertain temperature for a certain amount of time) that start to cause areduction in T_(c) (e.g., those that have been annealed or heatedbetween 100° C. and 150° C. for 1-10 minutes, but no longer and nohotter)—these can be useful for operational temperature 0<T_(op)<6 K;and (2) Components that have been annealed or heated under conditions(e.g., above a certain temperature for a certain amount of time) thatstart to cause a reduction in T_(c) (e.g., those that have been annealedor heated above 150° C. and/or for longer than 1-10 minutes)—these canbe useful for operational temperatures 0<T_(op)<2 K.

An integrated circuit is typically fabricated over an area known as achip or a die. In many instances, the density of circuit elements (i.e.,the density of metal wiring) is not uniform over the area of the die. Inmulti-layered circuits involving at least one stage of planarization,these non-uniformities in wiring density can result in non-uniformitiesin the surface(s) of the various layers. For an evenly appliedplanarization force, the rate at which a dielectric layer recedes duringplanarization may depend on the composition of the underlying layer(s).That is, a portion of a dielectric layer that overlies a metal structuremay recede at a different rate during planarization than a portion ofthe same dielectric layer that overlies another dielectric layer. Forexample, when a first dielectric layer that has a first portion carrieddirectly on a metal layer and a second portion carried directly on asecond dielectric layer is planarized, the resulting thickness of thefirst dielectric layer may not be uniform. In various embodiments, thenon-uniformities in the planarized surface may include pits, steps,protrusions, and/or a general curvature. Such non-uniformities canadversely affect the deposition of subsequent layers and/or adverselyaffect the operation of the integrated circuit. In particular,non-uniformities in the thickness of a dielectric layer can introducepotentially detrimental parametric spreads in the devices included inthe integrated circuit. In semiconductor fabrication practices, thesenon-uniformities may be mitigated by designing the integrated circuit toinclude idle (i.e., electrically inactive and unused) structures offiller metal in order to improve the uniformity of metal wiring densityover the area of the die. In accordance with the present systems andmethods, a similar approach may be adapted for use in superconductingintegrated circuits, where the structures of filler metal are formed ofa material that is superconducting below a critical temperature in orderto avoid introducing unwanted sources of thermal energy and/or magneticfields into the circuit.

In an embodiment, a series of Mx-Re-My multilayers can be deposited orgrown on a substrate. In between multilayer deposition/growth, or afterthe complete set of multilayers is deposited/grown, one or more etchingsteps can be used to form conductors, bonding pads, electrical devices,and circuits via the multilayers. Mx-Re-My multilayers can bedeposited/grown on the substrate, on an insulating or dielectric layer(e.g., SiO₂), or on a plurality of other layers such as a combination ofdielectric and metal layers. In some embodiments, the Mx-Re-Mymultilayer can be deposited/grown on a semiconducting substrate that canbe doped before or after Mx-Re-My multilayer deposition/growth. In somecases, a semiconducting device, circuit, or wire, can be electricallycoupled to a superconducting conductor formed from Mx-Re-My multilayers,or a superconducting Mx-Re-My conductor can be deposited/grown betweentwo or more circuits, electrical devices, and/or conductors formed fromcombinations of doped semiconductors, dielectrics, and/or conductors. Inother words, electrical components formed from Mx-Re-My multilayers, andoperated near or below T_(C) for the Mx-Re-My multilayers, can beintegrated with traditionally-fabricated electrical components.

FIG. 5 illustrates an embodiment of a method for using a high-T_(c)multilayer circuit. The method 500 can include providing asuperconducting multilayer circuit (Block 502) such as those describedthroughout this disclosure including at least a trilayer of anon-ferromagnetic conductor, Re electroplated to the underlying layer,and a capping layer of the same or a different non-ferromagneticconductor. The method 500 can also include providing a vacuum andrefrigeration chamber (Block 504) and cooling the circuit to at least4.2 K or at least 2.2 K (Block 506). The method 500 can further includepassing a superconducting current through the circuit (Block 508) andachieving 0 or nearly 0 resistive losses (Block 510). In some instances,one or more wire bonds and/or soldering connections can be made to thecircuit and as such the topmost non-ferromagnetic conductive layershould be conducive to such bonds without structural degradation andwithout degrading or substantially changing the T_(c) of the Relayer(s).

FIG. 6 illustrates an embodiment of a method for fabricating asuperconducting circuit that is superconducting at or above 4.2 K. Themethod 600 can include providing a substrate (Block 602) and applying afirst non-ferromagnetic conductive layer onto the substrate (Block 604).The method 600 can further include electroplating a second layer, Re,above the first layer to a thickness of between 10 nm to 1000 nm (Block608). The method can yet further include applying a thirdnon-ferromagnetic conductive layer onto the Re layer and encapsulatingthe Re layer to prevent oxidation of the Re layer (Block 610). Thesecond and third layers can form a Re-My pair, where My is anynon-ferromagnetic conductive layer, and can be the same or differentthan the conductor of the first layer. Additional ones of this pair oflayers can be formed between the first layer and the Re layer (optionalBlock 606) so that the eventual multilayer stack has the formMx-(Re-My)*Z-Re-My, where “Z” is a number of additional Re-My pairs.Each My layer above an Re layer can encase the previous Re layer, oronly the final My layer can encase all Re layers. Each layer can bepatterned to form a circuit (Block 612) and a wire bond or solderconnection can be formed between the third layer and another circuit(Block 614). The third layer material should be selected as a materialthat is immiscible with Re and has a high enough melting point to avoidstructural degradation during wire bonding. The superconducting circuitcan be arranged within a vacuum and/or refrigeration chamber that isconfigured to cool the superconducting circuit to at least 4.2 K or atleast 2.2 K (Block 616). It should be noted that the electroplating ofthe Re layer(s) can be performed in an aqueous solution. Any layersbonded to a Re layer should be immiscible with the Re layer. Not all Mylayers need be the same, but the outermost or capping layer should beapplicable to wire bonding, soldering connections, or other intendeduse, and preclude oxidation of any exposed Re layers.

Applying the first non-ferromagnetic conductive layer can be performedvia various additive processes, such as electroplating, sputterdeposition, and electroless plating, to name a few non-limitingexamples. Examples of the first non-ferromagnetic conductive layerinclude, but are not limited to, Cu, Au, Pt, Pd, Ni, Rh, Ru. In anembodiment, the first layer can be deposited on a wall of a multilayercircuit board via. This can occur via electroless plating. Whereproximitization of the first layer by the second layer, or whateverlayer is bonded to the first layer, is desired, the first layer can beless than 100 nm or less than 60 nm thick.

FIG. 7 illustrates embodiments of layer structures for the Mx-Re-Myelectroplated layers disclosed herein. FIG. 7A shows a cross section ofa multilayer planar structure, such as would be applied to a printedcircuit board. FIG. 7B shows a cross section of a multilayer planarstructure such as would be applied to form a wire or cable. In bothcases, the multilayer structure is formed on a substrate, such as PCB orsilicon for a printed circuit board or SoC, and a dielectric core in thecase of a wire or cable. At a minimum these structures can include afirst conductive layer M1, an electroplated Re layer, Re1, above that,and a capping layer M2. M1 and M2 may or may not be the same material.Additional pairs of Re and capping layers Mx can be added on this basetrilayer structure. Each additional Re electroplating should be followedby or capped with a final Mx or conductive layer. Although not shown,this same layering structure could be applied to the inside of a circuitboard via. In that case the multilayer structure would have a donut orcylinder shape with an outermost layer being M1 and the innermost layerbeing M2 or Mx.

Superconducting Vias

Since they were first introduced around the time of World War II,conventional printed circuit boards (“PCBs”) have simultaneously reducedin size and grown in sophistication. An important step in this evolutionwas the introduction of conductive vias to provide electricalcommunication between separate layers of a PCB. A via is an electricalconnection between layers in a physical electronic circuit (such as amultilayer PCB) that goes through the plane of one or more layers. Forstandard, copper-based PCBs a typical non-superconducting via is formedby drilling or etching a hole in a substrate that is aligned withcircuit structures on the top and bottom of the substrate, and possiblyalso with circuit structures within one or more inner layers of thesubstrate. One then coats the wall of the hole, first by a thinelectroless layer, followed by a thicker electroplated layer, both usinga non-superconducting metal, usually Cu. In the case of asuperconducting via, one can similarly form (e.g., drilling, etching) ahole through the substrate, electroless-plate the hole with a normalnon-superconducting metal using standard methods, and then electro-plateon top of the normal non-superconducting metal with a superconductingmetal (e.g., instead of Cu). The result is a superconducting path fromthe top to the bottom of the substrate using an easily-implemented,industry standard method. However, the non-superconducting metal forms abarrier to superconducting current trying to reach interior layers ofthe substrate.

Previous attempts to address this problem of making superconductingconnections to inner layers have been made, for instance, U.S. Pat. No.8,441,329 entitled “Input/Output Systems and Devices for Use withSuperconducting Based Computing Systems”, U.S. Pat. No. 8,008,991entitled “Systems, Methods and Apparatus for Electrical Filters”, andWO2018106942 entitled “Superconducting Printed Circuit Board RelatedSystems, Methods, and Apparatus”.

The WO2018106942 offers one solution—simply replace thenon-superconducting metal with a superconducting metal. Yet, whileseemingly simple in theory, in practice (from the standpoint of standardPCB fabrication procedures), actually making this replacement iscomplicated, many-stepped (some of which being unproven), and radicallydifferent from standard methods—in other words, undue experimentationwould be required to implement the replacement that WO2018106942theorizes. This is because the process described in that application isbased on the superconducting metals aluminum (Al) or possibly niobium(Nb), neither of which can be plated from aqueous solutions, theindustry standard. The application does mention the possibility ofelectroplating Al from ionic liquids, but then teaches away bydescribing how difficult this would be. The presence of water in thesolution itself, in atmosphere above the solution, and in the PCB boardmaterial being plated would need to be at the parts per million level,which is difficult to achieve, and the application presents nosuggestions for achieving this enabling requirement. Other methods ofdepositing Al, such as evaporation, sputtering, etc. are even moredifficult, requiring vacuum chambers and associated equipment. Theserequirements would be totally outside the complexity and cost ofequipment currently used to fabricate PCBs.

Because of these challenges, the vast majority of the application turnsto alternative means of providing a superconducting pathway to innerlayers of the PCB (e.g., FIGS. 2B-2E and FIG. 3). These additionalsolutions are provided in recognition that FIG. 1 is non-enabling to oneof skill in the art without undue experimentation. It should also benoted that WO2018106942 provides a long list of superconductors, butfails to mention Re as a replacement superconducting metal. Thisapplication also requires an annealing step, to laminate the two PCBhalves, after the vias have already been formed.

The herein described embodiments overcome these challenges and providesan enabling disclosure for providing a superconducting connection (e.g.,a via) to and between all interior and exterior layers of a PCB or othermultilayered circuit board by way of a true superconducting via.Additionally, the via coating can occur after the PCB or multilayeredcircuit board has been laminated. In these embodiments, T_(c) canbe >1.8 K and for PCB materials requiring lamination temperature <150°C., it can be equal to or greater than 4.2 K. A key aspect of thissolution is proximitization (or the proximity effect)—a phenomenon inwhich making a strong binding between a thin (e.g., less than 100 nm orless than 60 nm) non-superconductor or low-T_(c) superconductor and asuperconductor or high-T_(c) superconductor, respectively, causes thethinner material to take on, at least partially, the qualities of thesuperconducting or high-T_(c) material. See e.g., Clarke, John, TheProximity Effect Between Superconducting and Normal Thin Films in ZeroField, Journal de Physique, Colloque C 2, Supplement No. 2-3, Vol. 29,Fevrier-Mars 1968, pages C 2-3. It should also be noted thatimmiscibility between the two metals is important for the properoperation of the proximity effect. Accordingly, Re and standardmicroelectronics metals such as Cu, Au, Pt, Pd, Ni, Rh, Ru are stronglyinfluence by the proximity effect when the non-superconducting layer issufficiently thin. The thinner material is preferably between 60 nm and100 nm in thickness, since the proximity effect tends to fall offrapidly for greater thicknesses and thus some portions of the materialwould maintain their bulk properties.

In this disclosure, a thin conductor (e.g., Pd, Pt, Rh of less than 100nm or less than 60 nm) can be plated to the drilled hole (to interiorconductive and insulative material) by standard electroless plating(which is commonly used in the case of copper). Given this seedconductor layer, a thicker Re layer can then be electroplated to theseed layer (since without the conductive seed layer electroplatingdirectly to the insulative via sidewalls is not possible). Theelectroplated Re proximitizes the thin seed layer and can either converta non-superconductor (e.g., Cu) into a superconductor or convert alow-T_(c) superconductor (e.g., Rd) into a high-T_(c) superconductor. Inessence, this allows the superconducting current to superconduct throughthe seed layer and reach the inner layers of the multilayer circuitboard, and do so without the complex laminations shown in FIGS. 2B-2E ofthe WO2018106942 application. Also, Re vias connecting circuits on thetop and bottom of the board can be plated after all lamination (heating)steps have occurred, and thereby maintain high-T_(c).

FIG. 16 illustrates an embodiment of a via structure in a multilayer PCBor other multilayer circuit board using a superconducting via that iscoated after the multilayer structure has been laminated. The via 1600allows a superconducting path between a top and bottom of the PCB orother circuit board and optionally between at least one (and possiblyall) of the inner conducting layers that are intersected by the via.

Where a low-T_(c) layer is proximitized, the via 1600 makessuperconducting connections to “interior” traces through a low-T_(c)superconductor 1602 that is proximitized by a high-T_(c) superconductor1603. Specifically, arranging a high-T_(c) material in contact with alow T_(c) material can cause an increase in T_(c) in the low-T_(c)material. Here, the high-T_(c) via structure 1600 can include ahigh-T_(c) single or multilayer superconductor 1603 electroplated onto athin (e.g., less than 100 nm or less than 60 nm) electroless-plated,low-T_(c) superconductor 1602. These layers can also be referred to asthe inner wall 1603 and the outer wall 1602 of the via 1600. Even thoughthe outer wall 1602 is a low-T_(c) superconductor in isolation, it canbe proximitized by the high-T_(c) inner wall 1603 and therefore operateas a high-T_(c) superconductor. The via 1600 can further include ahigh-T_(c) electroplated single or multilayer superconductor 1601 on anexterior trace that makes direct high-T_(c) contact to the inner wall1602 of the via (referred to as an “exterior trace”). This layer 1601can either be coated in the same step as the inner wall 1603 of the viaas seen in FIG. 16, or these two layers can be separately coated as seenin FIG. 17. Because the inner wall 1602 has been proximitized and is nowhigh-T_(c), the high-T_(c) exterior trace 1601 can be said to make ahigh-T_(c) connection with the inner wall 1603 through the outer wall1602. The via 1600 can further include a high-T_(c) electroplated singleor multilayer superconductor 1604 on an interior trace that makes directhigh-T_(c) contact to the inner wall 1602 of the via (referred to as an“interior trace”). Because the inner wall 1602 has been proximitized andis now high-T_(c), the high-T_(c) interior trace 1601 can be said tomake a high-T_(c) connection with the inner wall 1603 through the outerwall 1602. Interior superconducting traces 1606 do not intersect the via1600 and so do not make electrical connection to any other traces. ThePCB or other circuit board can include a dielectric core 1607 that canbe solid or flexible and with or without multiple layers.

Where a non-superconducting layer is proximitized, the via 1600 makessuperconducting connections to “interior” traces through anon-superconducting layer 1602 that is proximitized by a superconductor1603. Specifically, arranging a superconductor in contact with anon-superconducting layer can cause the non-superconducting layer tobecome superconducting. Here, the via structure 1600 can include asingle or multilayer superconductor 1603 electroplated onto a thin(e.g., less than 100 nm or less than 60 nm) electroless-plated,non-superconducting layer 1602. These layers can also be referred to asthe inner wall 1603 and the outer wall 1602 of the via 1600. Even thoughthe outer wall 1602 is non-superconducting in isolation, it can beproximitized by the superconducting inner wall 1603 and therefore alsooperate as a superconductor. The via 1600 can further include a singleor multilayer superconductor 1601 on an exterior trace that makes directsuperconducting contact to the inner wall 1602 of the via (referred toas an “exterior trace”). This layer 1601 can either be coated in thesame step as the inner wall 1603 of the via as seen in FIG. 16, or thesetwo layers can be separately coated as seen in FIG. 17. Because theinner wall 1602 has been proximitized and is now superconducting, thesuperconducting exterior trace 1601 can be said to make asuperconducting connection with the inner wall 1603 through the outerwall 1602. The via 1600 can further include a single or multilayersuperconductor 1604 on an interior trace that makes directsuperconducting contact to the inner wall 1602 of the via (referred toas an “interior trace”). Because the inner wall 1602 has beenproximitized and is now superconducting, the superconducting interiortrace 1601 can be said to make a superconducting connection with theinner wall 1603 through the outer wall 1602. The via 1600 can alsoinclude one or more interior superconducting traces 1606 not makingcontact with either inner or outer walls 1603, 1602 of the via 1600. Themultilayer PCB or other circuit board can include a dielectric core 1607that can be solid or flexible and with or without multiple layers.

In some embodiments, where high-T_(c) operation is not needed, the outerwall 1602 can be a thin or sparse layer of a superconducting seed layersuch as Pd, that is plated to the insulative via 1600 wall viaelectroless plating. This would enable a superconducting path to theinner layers even without proximitization. In this case, the outer wall1602 could be thicker than the minimum thicknesses needed for the entirethickness of the outer wall 1602 to be proximitized (e.g., greater than100 nm or greater than 60 nm).

Those of skill in the art will appreciate that FIGS. 16 and 17 areillustrative only, and that this discussion of superconducting vias isequally applicable to all types of PCBs and circuit boards regardless ofthe number and structure of layers (and those without any layers).

FIG. 18 illustrates an embodiment of a superconducting resonance cavitywith an inner wall formed from a thin low-T_(c) superconductor that isproximitized by a good electrical bond with a high-T_(c) superconductor.This structure 1800 can have superconducting surfaces formed by platinga thin material (e.g., Pd, Rh, or Pt) 1801 directly atop a Reelectroplated layer 1802 to form a low loss cavity resonator throughproximitization of the thin layer 1802. The conductive block that theresonance cavity 1800 is formed from may not be superconducting (e.g.,Cu). A cavity can be drilled/milled out of the block of material or canbe formed via casting or other metallurgical processes. A firstelectroplated layer 1801 can be formed inside the cavity using ahigh-T_(c) superconductor such as Re. This first layer 1801 can beformed as a single or multilayer structure. A thin second layer 1802 canthen be electroplated, or plated via an electroless process, using alow-T_(c) superconductor (e.g., Pd, Rh, or Pt). However, this secondlayer 1802, if appropriately thin, can be proximitized by the firstlayer 1802, such that both layers 1801, 1802 operate as a high-T_(c)superconductor. Typically, the inner layer 1802 should be less than 100nm thick, or less than 60 nm thick to optimize the proximity effect. Thesecond layer 1802 can be referred to as a proximitized material.

FIG. 19 illustrates a superconducting circuit system. The system 1900can be implemented as a wire (not shown) or circuit board in a vacuumchamber 1904. The chamber can be evacuated via one or more vacuumdevices 1906 and cooled via one or more cooling elements 1910, 1912. Asuperconducting multilayer structure 1902 can be arranged within thechamber 1904. The cooling element 1912 can be directly coupled to thechamber 1904 while the optional cooling element 1910 can be directlycoupled to the superconducting multilayer structure 1902. Thesuperconducting multilayer structure 1902 can operate at or below 4.2 Kor at or below 2.2 K and can pass superconducting current between asignal source 1914 and a load (not shown) or other circuitry. Forinstance, an optional wire bond 1905 or solder bond (not shown) can beformed at one end of the superconducting multilayer structure 1902 tocouple current into a load or other circuit. An opposing end of thesuperconducting multilayer structure 1902 can also include a wire bond1904 or solder bond (not shown) that provides a current path between thesignal source 1914 and the superconducting multilayer structure 1902.The signal source 1914 can be arranged inside or outside of the chamber1904.

The superconducting multilayer structure 1902 can include any of themultilayer structures described herein. For instance, it can include asubstrate or core having an initial Mx-Re-My trilayer followed by anoptional number of Re-My bilayers thereafter. The illustratedsuperconducting multilayer structure 1902 includes a first conductivelayer, an electroplated Re layer, and a capping layer, though multiplesof this trio can also be implemented. The Re layer can be a high-T_(c)layer when the system 1900 is operational (e.g., cooling the chamber1900, or at least the superconducting multilayer structure 1902, to orbelow 4.2 K or to or below 2.2 K). In an embodiment, the first layer inthe stack can be a non-ferromagnetic conductive layer bonded to thesubstrate. The second layer can be a Re layer bonded to the first layervia electroplating. The Re layer can have a thickness of between 10 nmand 1000 nm (though a thicker Re layer is desirable whereproximitization is intended). The third layer can be a non-ferromagneticlayer bonded to the Re layer and encapsulating the Re layer to preventoxidization thereof. Each of these layers can be independently orsimultaneously patterned to create at least a portion of asuperconducting circuit. Patterning can include additive processes likedeposition, where a mask dictates those portions of each layer that donot see deposition, or subtractive processes like etching, where a maskdetermines those portions of each layer that remain after etching.

In an embodiment, the superconducting multilayer structure 1902 can be amultilayered circuit board including one or more vias that pass from atop to a bottom of the substrate and/or to an inner or middle layer ofthe substrate. The vias can be coated with the same or a different setof multilayers as the top and/or bottom surfaces of the substrate. Tofacilitate proximitization of the first layer (bonded to theinsulating/dielectric substrate), the first layer can be less than 100nm thick or less than 60 nm thick. Where the first layer isnon-superconducting in isolation and the second layer issuperconducting, the first layer may become superconducting when bondedto the second superconducting layer. Where the first layer is alow-T_(c) superconductor, and the second layer is a high-T_(c)superconductor, the first layer may become a high-T_(c) layer whenbonded to the second high-T_(c) layer.

Some non-limiting examples of vacuum devices include turbo (orturbomolecular) pumps, diffusion pumps, ion pumps, and linearcompressors. One non-limiting examples of cooling elements includecryoheads. The combination of chamber 1904, pump 1906, and coolingelement 1910, 1912 can be referred to as a low-temperature system andsome non-limiting examples include a liquid helium refrigerator (orhelium-3 or helium-4 refrigerator), liquid hydrogen refrigerator,dilution refrigerator, an adiabatic demagnetization refrigerator (ADR),liquid nitrogen refrigerator, regenerative-cooling refrigerator,multi-component refrigerant refrigerators, Kleemenko cyclerefrigerators, pulse tube refrigerators, liquid helium cryopumps, andpolycold refrigeration systems.

As used herein, the recitation of “at least one of A, B and C” isintended to mean “either A, B, C or any combination of A, B and C.” Theprevious description of the disclosed embodiments is provided to enableany person skilled in the art to make or use the present disclosure.Various modifications to these embodiments will be readily apparent tothose skilled in the art, and the generic principles defined herein maybe applied to other embodiments without departing from the spirit orscope of the disclosure. Thus, the present disclosure is not intended tobe limited to the embodiments shown herein but is to be accorded thewidest scope consistent with the principles and novel features disclosedherein.

CITATIONS

-   [1] 0. A. Mukhanov, IEEE Trans. Appl. Supercond. 21, 760 (2011).-   [2] Q. P. Herr, A. Y. Herr, 0. T. Oberg, and A. G. Ioannidis, J.    Appl. Phys. 109, Art. No. 103903 (2011).-   [3] M. A. Manheimer, IEEE Trans. Appl. Supercond. 25, Art. No.    1301704 (2015).-   [4] D. S. Holmes, A. L. Ripple, and M. A. Manheimer, IEEE Trans.    Appl. Supercond. 23, Art. No. 1701610 (2013).-   [5] M. H. Devoret and R. J. Schoelkopf, Science 339, 1169 (2013).-   [6] V. Kotsubo, R. Radebaugh, P. Hendershott, M. Bon-czyski, B.    Wilson, S. W. Nam, and J. N. Ullom, IEEE Trans. Appl. Supercond. 27,    Art. No 9500405 (2017), ISSN 1051-8223.-   [7] R. Radebaugh, J. Phys.: Condens. Matter 21, Art. No. 164219    (2009).-   [8] W. M. Haynes, CRC Handbook of Chemistry and Physics (92nd ed.)    (CRC Press, U.S.A., 2011), ISBN ISBN 1439855110.-   [9] M. P. Weides, J. S. Kline, M. R. Vissers, M. 0. Sandberg, D. S.    Wisbey, B. R. Johnson, T. A. Ohki, and D. P. Pappas, Appl. Phys.    Lett. 99, Art. No. 262502 (2011).-   [10] M. Mito, H. Matsui, K. Tsuruta, T. Yamaguchi, K. Naka-mura, H.    Deguchi, N. Shirakawa, H. Adachi, T. Ya-masaki, H. Iwaoka, et al.,    Sci. Rep. 6, Art. No. 36337 (2016).-   [11] J. G. Daunt and T. S. Smith, Phys. Rev 88, 309 (1952).    [12] C. W. Chu, W. L. McMillan, and H. L. Luo, Phys. Rev. B 3, 3757    (1971).-   [12] C. W. Chu, W. L. McMillan, and H. L. Luo, Phys. Rev. B 3, 3757    (1971).-   [13] L. R. Testardi, J. J. Hauser, and M. H. Read, Solid State Comm.    9, 1829 (1971).-   [14] S. Sundar, S. Banik, L. S. S. Chandra, M. K. Chattopad-hyay, T.    Ganguli, G. S. Lodha, S. K. Pandey, D. M. Phase, and S. B. Roy, J.    Phys.: Condens. Matter 28, Art. No. 315502 (2016).-   [15] V. Singh, B. H. Schneider, S. J. Bosman, E. P. J. Merkx,    and G. A. Steele, Appl. Phys. Lett. 105, Art. No. 222601 (2014).-   [16] C. G. Fink and P. Deren, Trans. Electrochem. Soc. 66, 471    (1934).-   [17] R. Levi, Rhenium plating (1952), U.S. Pat. No. 2,616,840, URL    https:I/patentimages. storage.googleapis.com/8c/58/83/4352341 20f    94b3/U.S. Pat. No. 2,616,840.pdf.-   [18] Y. N. Sadana and Z. Z. Wang, 37, 419 (1989).-   [19] A. B. Gamburg, Yu. D. and. Drovosekovz and T. P. Puryaeva,    Russian Journal of Electrochemistry 51, 376 (2015).-   [20] V. V. Zhulikov and Y. D. Gamburg, Russian Journal of    Electrochemistry 52, 847 (2016).-   [21] S.-Y. Chang, L.-P. Liang, L.-C. Kao, and C.-F. Lin, Jour-nal of    The Electrochemical Society 162, D96 (2015).-   [22] J. Mazierska, M. V. Jacob, D. Ledenyov, and J. Krupk, in 2005    Asia-Pacific Microwave Conference Proceedings (2005), vol. 4, p.    2370.-   [23] B. Knook, W. Star, H. V. Rongen, and G. V. den Berg, Physica    30, 1124 (1964), ISSN 0031-8914, URL    http://www.sciencedirect.com/science/article/pii/003189146490103×.-   [24] H. Okamoto and T. B. Massalski, Bulletin of Alloy Phase    Diagrams 5, 383 (1984), ISSN 0197-0216, URL    https://doi.org/10.1007/BF02872959.-   [25] F. A. Shunk, Constitution of Binary Alloys, Second Sup-plement    (McGraw-Hill Book Company, U.S.A., 1985), ISBN 0-931690-20-×.-   [26] B. Predel, Au—Re (Gold-Rhenium) (Springer Berlin Hei-delberg,    Berlin, Heidelberg, 1991), pp. 1-1, ISBN 978-3-540-39444-0, URL    https://doi.org/10.1007/10000866_311.-   [27] C. Kittel, Introduction to Solid State Physics, 5th edition    (John Wiley & Sons, Inc., U.S.A., 1976), ISBN ISBN 0-471-49024-5.-   [28] M. Tinkham, Introduction to Superconductivit y, Second Edition    (Dover Publications, Mineola, N.Y., 1996), ISBN 978-0-486-43503-9,    0-486-43503-2.-   [29] S. Probst, F. B. Song, P. A. Bushey, A. V. Ustinov, and M.    Weides, Rev. of Sci. Instr. 86, 024706 (2015), ISSN 0197-0216.-   [30] D. P. Pappas, M. R. Vissers, D. S. Wisbey, J. S. Kline, and J.    Gao, IEEE Trans. Appl. Supercond. 21, 871 (2011).-   [31] H. M. Syed, C. Webb, and E. M. Gray, Progress in Solid State    Chemistry 44, 20 (2016).-   [32] B. Knook, W. M. Star, H. J. M. Van Rongen, G. J. Van Den Berg,    Physica 30, 1124-1130, Communication No. 339a from the Kamerlingh    Onnes Laboratorium, (1964).

What is claimed is:
 1. A method of fabricating a superconductingcircuit, the method comprising: providing a substrate; applying a firstconductive layer onto the substrate; electroplating a second Re layerabove the first layer to a thickness of between 10 nm to 1000 nm;applying a third conductive layer onto the second Re layer andencapsulating the second Re layer; making a wire bond or solderconnection between the third conductive layer and another circuit;wherein the superconducting circuit is superconducting at or above 4.2K.2. The method of claim 1, wherein the Re is amorphous.
 3. The method ofclaim 1, wherein one or more additional pairs of Re and conductivelayers are formed before the second and third layers and wherein theseone or more additional pairs of layers are arranged between the firstand second layers.
 4. The method of claim 1, wherein the electroplatingoccurs in an aqueous solution.
 5. The method of claim 1, wherein thefirst layer is deposited on a wall of a multilayer circuit board viausing electroless plating.
 6. The method of claim 5, wherein the firstlayer is less than 60 nm.
 7. The method of claim 1, wherein the firstand third layers are immiscible with the second Re layer.
 8. The methodof claim 1, wherein the substrate has a circular cross section and isthe core of a wire or cable.
 9. The method of claim 1, wherein thecircuit does not exceed 150° C.
 10. The method of claim 8, wherein thecircuit does not exceed 100° C. for more than one hour.
 11. The methodof claim 1, wherein, once the third conductive layer is applied, thesuperconducting circuit is annealed at 100-150 C for 1-10 minutes. 12.The method of claim 1, wherein the electroplating is performed atatmospheric or near-atmospheric pressure.
 13. The method of claim 1,wherein the third conductive layer is applied at once to minimizeoxidization of the second Re layer.
 14. The method of claim 1, whereineither or both of the first and third conductive layers areindependently chosen from the group comprising Cu, Au, Pt, Pd, Ni, Rh,and Ru.
 15. The method of claim 14, wherein the first conductive layeris Au, Cu, Ni, or Pd.
 16. The method of claim 1, further comprisingarranging the superconducting circuit within a chamber configured tocool the superconducting circuit to at least 4.2 K.
 17. The method ofclaim 1, wherein the first layer is less than 60 nm in thickness, andwherein the first layer in isolation is non-superconducting, but whenbonded to the second Re layer is superconducting via proximitization.18. The method of claim 17, wherein the first layer is less than 60 nmin thickness, and wherein the first layer in isolation is notsuperconducting above 2 K, but when bonded to the second Re layer issuperconducting at and above 4.2 K via proximitization.
 19. Asuperconducting circuit system comprising: a means for maintaining thecircuit at or below 6.0 K; a substrate; a first conductive layer bondedto the substrate; a second amorphous Re layer deposited over the firstconductive layer using electroplating, and the second amorphous Re layerhaving a thickness of between 10 nm and 1000 nm; and a third conductivelayer bonded to the second amorphous Re layer and encapsulating thesecond Re layer, wherein the first and third layers are immiscible withthe second amorphous Re layer.
 20. A superconducting circuit systemcomprising: a means for maintaining the circuit at or below 6.0 K; asubstrate; a first conductive layer bonded to the substrate; a secondamorphous Re layer deposited over the first conductive layer usingelectroplating, and the second amorphous Re layer having a thickness ofbetween 10 nm and 1000 nm; and a third conductive layer bonded to thesecond amorphous Re layer and encapsulating the second amorphous Relayer, wherein the first layer is less than 60 nm in thickness, andwherein the first conductive layer in isolation is not superconductingabove 2 K, but when bonded to the second amorphous Re layer issuperconducting at and above 4.2 K via proximitization